Moduli spaces of vector bundles over ruled surfaces

Abstract

We study moduli spaces $M(c_1,c_2,d,r)$ of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants $c_1,c_2,d,r$ over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the space $M(c_1,c_2,d,r)$ and we apply this result to the moduli spaces ${\cal M}_L(c_1,c_2)$ of stable bundles, where $L$ is an ample line bundle on the ruled surface.